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Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be –8x, where A and B are arbitrary constants - Mathematics

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प्रश्न

Find the differential equation corresponding to the family of curves represented by the equation y = Ae8x + Be 8x, where A and B are arbitrary constants

बेरीज
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उत्तर

Given y = Ae8x + Be8x  .........(1)

Where A and B are arbitrary constants differentiating equation (1) twice successively because we have two arbitrary constant, we get

`("d"y)/("d"x)` = Ae8x + Be–8x (– 8)

`("d"y)/("d"x)` = 8Ae8x – 8Be8x  ........(2)

`("d"^2y)/("d"x^2)` = 8Ae8x (8) – Be8x (– 8)

= 64Ae8x + 64Be8x

= 64[Ae8x + Be8x]  .........(3)

Substituting equation (1) in eqn (3), we get

`("d"^2y)/("d"x^2)` = 64y

`("d"^2y)/("d"x^2) - 64y` = 0 is the required differential equation.

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पाठ 10: Ordinary Differential Equations - Exercise 10.3 [पृष्ठ १५४]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 10 Ordinary Differential Equations
Exercise 10.3 | Q 7 | पृष्ठ १५४

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